Properties

Label 320.2.o.d.287.1
Level $320$
Weight $2$
Character 320.287
Analytic conductor $2.555$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 320.287
Dual form 320.2.o.d.223.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} +1.00000i q^{9} +4.00000 q^{11} +(3.00000 + 3.00000i) q^{13} +(3.00000 + 1.00000i) q^{15} +(-3.00000 - 3.00000i) q^{17} -6.00000i q^{19} +2.00000i q^{21} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -2.00000 q^{29} -6.00000i q^{31} +(4.00000 - 4.00000i) q^{33} +(-3.00000 - 1.00000i) q^{35} +(3.00000 - 3.00000i) q^{37} +6.00000 q^{39} +6.00000 q^{41} +(-3.00000 + 3.00000i) q^{43} +(-2.00000 + 1.00000i) q^{45} +(-9.00000 + 9.00000i) q^{47} +5.00000i q^{49} -6.00000 q^{51} +(-5.00000 - 5.00000i) q^{53} +(4.00000 + 8.00000i) q^{55} +(-6.00000 - 6.00000i) q^{57} +10.0000i q^{59} -12.0000i q^{61} +(-1.00000 - 1.00000i) q^{63} +(-3.00000 + 9.00000i) q^{65} +(-9.00000 - 9.00000i) q^{67} -6.00000 q^{69} -6.00000i q^{71} +(5.00000 - 5.00000i) q^{73} +(1.00000 + 7.00000i) q^{75} +(-4.00000 + 4.00000i) q^{77} +5.00000 q^{81} +(-3.00000 + 3.00000i) q^{83} +(3.00000 - 9.00000i) q^{85} +(-2.00000 + 2.00000i) q^{87} -6.00000 q^{91} +(-6.00000 - 6.00000i) q^{93} +(12.0000 - 6.00000i) q^{95} +(-7.00000 - 7.00000i) q^{97} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} + 2q^{5} - 2q^{7} + O(q^{10}) \) \( 2q + 2q^{3} + 2q^{5} - 2q^{7} + 8q^{11} + 6q^{13} + 6q^{15} - 6q^{17} - 6q^{23} - 6q^{25} + 8q^{27} - 4q^{29} + 8q^{33} - 6q^{35} + 6q^{37} + 12q^{39} + 12q^{41} - 6q^{43} - 4q^{45} - 18q^{47} - 12q^{51} - 10q^{53} + 8q^{55} - 12q^{57} - 2q^{63} - 6q^{65} - 18q^{67} - 12q^{69} + 10q^{73} + 2q^{75} - 8q^{77} + 10q^{81} - 6q^{83} + 6q^{85} - 4q^{87} - 12q^{91} - 12q^{93} + 24q^{95} - 14q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 1.00000i 0.577350 0.577350i −0.356822 0.934172i \(-0.616140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 0 0
\(5\) 1.00000 + 2.00000i 0.447214 + 0.894427i
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i \(-0.0497784\pi\)
−0.155747 + 0.987797i \(0.549778\pi\)
\(14\) 0 0
\(15\) 3.00000 + 1.00000i 0.774597 + 0.258199i
\(16\) 0 0
\(17\) −3.00000 3.00000i −0.727607 0.727607i 0.242536 0.970143i \(-0.422021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 6.00000i 1.37649i −0.725476 0.688247i \(-0.758380\pi\)
0.725476 0.688247i \(-0.241620\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) 0 0
\(23\) −3.00000 3.00000i −0.625543 0.625543i 0.321400 0.946943i \(-0.395847\pi\)
−0.946943 + 0.321400i \(0.895847\pi\)
\(24\) 0 0
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 6.00000i 1.07763i −0.842424 0.538816i \(-0.818872\pi\)
0.842424 0.538816i \(-0.181128\pi\)
\(32\) 0 0
\(33\) 4.00000 4.00000i 0.696311 0.696311i
\(34\) 0 0
\(35\) −3.00000 1.00000i −0.507093 0.169031i
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −3.00000 + 3.00000i −0.457496 + 0.457496i −0.897833 0.440337i \(-0.854859\pi\)
0.440337 + 0.897833i \(0.354859\pi\)
\(44\) 0 0
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 0 0
\(47\) −9.00000 + 9.00000i −1.31278 + 1.31278i −0.393431 + 0.919354i \(0.628712\pi\)
−0.919354 + 0.393431i \(0.871288\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) −5.00000 5.00000i −0.686803 0.686803i 0.274721 0.961524i \(-0.411414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) 0 0
\(55\) 4.00000 + 8.00000i 0.539360 + 1.07872i
\(56\) 0 0
\(57\) −6.00000 6.00000i −0.794719 0.794719i
\(58\) 0 0
\(59\) 10.0000i 1.30189i 0.759125 + 0.650945i \(0.225627\pi\)
−0.759125 + 0.650945i \(0.774373\pi\)
\(60\) 0 0
\(61\) 12.0000i 1.53644i −0.640184 0.768221i \(-0.721142\pi\)
0.640184 0.768221i \(-0.278858\pi\)
\(62\) 0 0
\(63\) −1.00000 1.00000i −0.125988 0.125988i
\(64\) 0 0
\(65\) −3.00000 + 9.00000i −0.372104 + 1.11631i
\(66\) 0 0
\(67\) −9.00000 9.00000i −1.09952 1.09952i −0.994466 0.105059i \(-0.966497\pi\)
−0.105059 0.994466i \(-0.533503\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) 5.00000 5.00000i 0.585206 0.585206i −0.351123 0.936329i \(-0.614200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) 0 0
\(75\) 1.00000 + 7.00000i 0.115470 + 0.808290i
\(76\) 0 0
\(77\) −4.00000 + 4.00000i −0.455842 + 0.455842i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −3.00000 + 3.00000i −0.329293 + 0.329293i −0.852318 0.523025i \(-0.824804\pi\)
0.523025 + 0.852318i \(0.324804\pi\)
\(84\) 0 0
\(85\) 3.00000 9.00000i 0.325396 0.976187i
\(86\) 0 0
\(87\) −2.00000 + 2.00000i −0.214423 + 0.214423i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) −6.00000 6.00000i −0.622171 0.622171i
\(94\) 0 0
\(95\) 12.0000 6.00000i 1.23117 0.615587i
\(96\) 0 0
\(97\) −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i \(-0.417612\pi\)
−0.966691 + 0.255948i \(0.917612\pi\)
\(98\) 0 0
\(99\) 4.00000i 0.402015i
\(100\) 0 0
\(101\) 8.00000i 0.796030i 0.917379 + 0.398015i \(0.130301\pi\)
−0.917379 + 0.398015i \(0.869699\pi\)
\(102\) 0 0
\(103\) −11.0000 11.0000i −1.08386 1.08386i −0.996145 0.0877167i \(-0.972043\pi\)
−0.0877167 0.996145i \(-0.527957\pi\)
\(104\) 0 0
\(105\) −4.00000 + 2.00000i −0.390360 + 0.195180i
\(106\) 0 0
\(107\) 3.00000 + 3.00000i 0.290021 + 0.290021i 0.837088 0.547068i \(-0.184256\pi\)
−0.547068 + 0.837088i \(0.684256\pi\)
\(108\) 0 0
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 0 0
\(111\) 6.00000i 0.569495i
\(112\) 0 0
\(113\) −3.00000 + 3.00000i −0.282216 + 0.282216i −0.833992 0.551776i \(-0.813950\pi\)
0.551776 + 0.833992i \(0.313950\pi\)
\(114\) 0 0
\(115\) 3.00000 9.00000i 0.279751 0.839254i
\(116\) 0 0
\(117\) −3.00000 + 3.00000i −0.277350 + 0.277350i
\(118\) 0 0
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 6.00000 6.00000i 0.541002 0.541002i
\(124\) 0 0
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) −5.00000 + 5.00000i −0.443678 + 0.443678i −0.893246 0.449568i \(-0.851578\pi\)
0.449568 + 0.893246i \(0.351578\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) 6.00000 + 6.00000i 0.520266 + 0.520266i
\(134\) 0 0
\(135\) −4.00000 + 12.0000i −0.344265 + 1.03280i
\(136\) 0 0
\(137\) −3.00000 3.00000i −0.256307 0.256307i 0.567243 0.823550i \(-0.308010\pi\)
−0.823550 + 0.567243i \(0.808010\pi\)
\(138\) 0 0
\(139\) 6.00000i 0.508913i −0.967084 0.254457i \(-0.918103\pi\)
0.967084 0.254457i \(-0.0818966\pi\)
\(140\) 0 0
\(141\) 18.0000i 1.51587i
\(142\) 0 0
\(143\) 12.0000 + 12.0000i 1.00349 + 1.00349i
\(144\) 0 0
\(145\) −2.00000 4.00000i −0.166091 0.332182i
\(146\) 0 0
\(147\) 5.00000 + 5.00000i 0.412393 + 0.412393i
\(148\) 0 0
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 0 0
\(153\) 3.00000 3.00000i 0.242536 0.242536i
\(154\) 0 0
\(155\) 12.0000 6.00000i 0.963863 0.481932i
\(156\) 0 0
\(157\) 3.00000 3.00000i 0.239426 0.239426i −0.577186 0.816612i \(-0.695849\pi\)
0.816612 + 0.577186i \(0.195849\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) 9.00000 9.00000i 0.704934 0.704934i −0.260531 0.965465i \(-0.583898\pi\)
0.965465 + 0.260531i \(0.0838976\pi\)
\(164\) 0 0
\(165\) 12.0000 + 4.00000i 0.934199 + 0.311400i
\(166\) 0 0
\(167\) 3.00000 3.00000i 0.232147 0.232147i −0.581441 0.813588i \(-0.697511\pi\)
0.813588 + 0.581441i \(0.197511\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) 0 0
\(173\) 15.0000 + 15.0000i 1.14043 + 1.14043i 0.988372 + 0.152057i \(0.0485898\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 0 0
\(175\) −1.00000 7.00000i −0.0755929 0.529150i
\(176\) 0 0
\(177\) 10.0000 + 10.0000i 0.751646 + 0.751646i
\(178\) 0 0
\(179\) 2.00000i 0.149487i 0.997203 + 0.0747435i \(0.0238138\pi\)
−0.997203 + 0.0747435i \(0.976186\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −12.0000 12.0000i −0.887066 0.887066i
\(184\) 0 0
\(185\) 9.00000 + 3.00000i 0.661693 + 0.220564i
\(186\) 0 0
\(187\) −12.0000 12.0000i −0.877527 0.877527i
\(188\) 0 0
\(189\) −8.00000 −0.581914
\(190\) 0 0
\(191\) 6.00000i 0.434145i −0.976156 0.217072i \(-0.930349\pi\)
0.976156 0.217072i \(-0.0696508\pi\)
\(192\) 0 0
\(193\) 5.00000 5.00000i 0.359908 0.359908i −0.503871 0.863779i \(-0.668091\pi\)
0.863779 + 0.503871i \(0.168091\pi\)
\(194\) 0 0
\(195\) 6.00000 + 12.0000i 0.429669 + 0.859338i
\(196\) 0 0
\(197\) −5.00000 + 5.00000i −0.356235 + 0.356235i −0.862423 0.506188i \(-0.831054\pi\)
0.506188 + 0.862423i \(0.331054\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −18.0000 −1.26962
\(202\) 0 0
\(203\) 2.00000 2.00000i 0.140372 0.140372i
\(204\) 0 0
\(205\) 6.00000 + 12.0000i 0.419058 + 0.838116i
\(206\) 0 0
\(207\) 3.00000 3.00000i 0.208514 0.208514i
\(208\) 0 0
\(209\) 24.0000i 1.66011i
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) −6.00000 6.00000i −0.411113 0.411113i
\(214\) 0 0
\(215\) −9.00000 3.00000i −0.613795 0.204598i
\(216\) 0 0
\(217\) 6.00000 + 6.00000i 0.407307 + 0.407307i
\(218\) 0 0
\(219\) 10.0000i 0.675737i
\(220\) 0 0
\(221\) 18.0000i 1.21081i
\(222\) 0 0
\(223\) 13.0000 + 13.0000i 0.870544 + 0.870544i 0.992532 0.121987i \(-0.0389267\pi\)
−0.121987 + 0.992532i \(0.538927\pi\)
\(224\) 0 0
\(225\) −4.00000 3.00000i −0.266667 0.200000i
\(226\) 0 0
\(227\) 11.0000 + 11.0000i 0.730096 + 0.730096i 0.970639 0.240543i \(-0.0773255\pi\)
−0.240543 + 0.970639i \(0.577325\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) −15.0000 + 15.0000i −0.982683 + 0.982683i −0.999853 0.0171699i \(-0.994534\pi\)
0.0171699 + 0.999853i \(0.494534\pi\)
\(234\) 0 0
\(235\) −27.0000 9.00000i −1.76129 0.587095i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) −7.00000 + 7.00000i −0.449050 + 0.449050i
\(244\) 0 0
\(245\) −10.0000 + 5.00000i −0.638877 + 0.319438i
\(246\) 0 0
\(247\) 18.0000 18.0000i 1.14531 1.14531i
\(248\) 0 0
\(249\) 6.00000i 0.380235i
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) −12.0000 12.0000i −0.754434 0.754434i
\(254\) 0 0
\(255\) −6.00000 12.0000i −0.375735 0.751469i
\(256\) 0 0
\(257\) −3.00000 3.00000i −0.187135 0.187135i 0.607321 0.794456i \(-0.292244\pi\)
−0.794456 + 0.607321i \(0.792244\pi\)
\(258\) 0 0
\(259\) 6.00000i 0.372822i
\(260\) 0 0
\(261\) 2.00000i 0.123797i
\(262\) 0 0
\(263\) 9.00000 + 9.00000i 0.554964 + 0.554964i 0.927869 0.372906i \(-0.121638\pi\)
−0.372906 + 0.927869i \(0.621638\pi\)
\(264\) 0 0
\(265\) 5.00000 15.0000i 0.307148 0.921443i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i 0.998153 + 0.0607457i \(0.0193479\pi\)
−0.998153 + 0.0607457i \(0.980652\pi\)
\(272\) 0 0
\(273\) −6.00000 + 6.00000i −0.363137 + 0.363137i
\(274\) 0 0
\(275\) −12.0000 + 16.0000i −0.723627 + 0.964836i
\(276\) 0 0
\(277\) 15.0000 15.0000i 0.901263 0.901263i −0.0942828 0.995545i \(-0.530056\pi\)
0.995545 + 0.0942828i \(0.0300558\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) 0 0
\(285\) 6.00000 18.0000i 0.355409 1.06623i
\(286\) 0 0
\(287\) −6.00000 + 6.00000i −0.354169 + 0.354169i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) −14.0000 −0.820695
\(292\) 0 0
\(293\) −1.00000 1.00000i −0.0584206 0.0584206i 0.677293 0.735714i \(-0.263153\pi\)
−0.735714 + 0.677293i \(0.763153\pi\)
\(294\) 0 0
\(295\) −20.0000 + 10.0000i −1.16445 + 0.582223i
\(296\) 0 0
\(297\) 16.0000 + 16.0000i 0.928414 + 0.928414i
\(298\) 0 0
\(299\) 18.0000i 1.04097i
\(300\) 0 0
\(301\) 6.00000i 0.345834i
\(302\) 0 0
\(303\) 8.00000 + 8.00000i 0.459588 + 0.459588i
\(304\) 0 0
\(305\) 24.0000 12.0000i 1.37424 0.687118i
\(306\) 0 0
\(307\) 15.0000 + 15.0000i 0.856095 + 0.856095i 0.990876 0.134780i \(-0.0430329\pi\)
−0.134780 + 0.990876i \(0.543033\pi\)
\(308\) 0 0
\(309\) −22.0000 −1.25154
\(310\) 0 0
\(311\) 18.0000i 1.02069i 0.859971 + 0.510343i \(0.170482\pi\)
−0.859971 + 0.510343i \(0.829518\pi\)
\(312\) 0 0
\(313\) 1.00000 1.00000i 0.0565233 0.0565233i −0.678280 0.734803i \(-0.737274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 0 0
\(315\) 1.00000 3.00000i 0.0563436 0.169031i
\(316\) 0 0
\(317\) 3.00000 3.00000i 0.168497 0.168497i −0.617822 0.786318i \(-0.711985\pi\)
0.786318 + 0.617822i \(0.211985\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −18.0000 + 18.0000i −1.00155 + 1.00155i
\(324\) 0 0
\(325\) −21.0000 + 3.00000i −1.16487 + 0.166410i
\(326\) 0 0
\(327\) 18.0000 18.0000i 0.995402 0.995402i
\(328\) 0 0
\(329\) 18.0000i 0.992372i
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 0 0
\(333\) 3.00000 + 3.00000i 0.164399 + 0.164399i
\(334\) 0 0
\(335\) 9.00000 27.0000i 0.491723 1.47517i
\(336\) 0 0
\(337\) 25.0000 + 25.0000i 1.36184 + 1.36184i 0.871576 + 0.490261i \(0.163099\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 6.00000i 0.325875i
\(340\) 0 0
\(341\) 24.0000i 1.29967i
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) −6.00000 12.0000i −0.323029 0.646058i
\(346\) 0 0
\(347\) −17.0000 17.0000i −0.912608 0.912608i 0.0838690 0.996477i \(-0.473272\pi\)
−0.996477 + 0.0838690i \(0.973272\pi\)
\(348\) 0 0
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) 24.0000i 1.28103i
\(352\) 0 0
\(353\) −15.0000 + 15.0000i −0.798369 + 0.798369i −0.982838 0.184469i \(-0.940943\pi\)
0.184469 + 0.982838i \(0.440943\pi\)
\(354\) 0 0
\(355\) 12.0000 6.00000i 0.636894 0.318447i
\(356\) 0 0
\(357\) 6.00000 6.00000i 0.317554 0.317554i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) 0 0
\(363\) 5.00000 5.00000i 0.262432 0.262432i
\(364\) 0 0
\(365\) 15.0000 + 5.00000i 0.785136 + 0.261712i
\(366\) 0 0
\(367\) 11.0000 11.0000i 0.574195 0.574195i −0.359103 0.933298i \(-0.616917\pi\)
0.933298 + 0.359103i \(0.116917\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 10.0000 0.519174
\(372\) 0 0
\(373\) 3.00000 + 3.00000i 0.155334 + 0.155334i 0.780496 0.625161i \(-0.214967\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(374\) 0 0
\(375\) −13.0000 + 9.00000i −0.671317 + 0.464758i
\(376\) 0 0
\(377\) −6.00000 6.00000i −0.309016 0.309016i
\(378\) 0 0
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) 0 0
\(381\) 10.0000i 0.512316i
\(382\) 0 0
\(383\) 21.0000 + 21.0000i 1.07305 + 1.07305i 0.997113 + 0.0759373i \(0.0241949\pi\)
0.0759373 + 0.997113i \(0.475805\pi\)
\(384\) 0 0
\(385\) −12.0000 4.00000i −0.611577 0.203859i
\(386\) 0 0
\(387\) −3.00000 3.00000i −0.152499 0.152499i
\(388\) 0 0
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 18.0000i 0.910299i
\(392\) 0 0
\(393\) 4.00000 4.00000i 0.201773 0.201773i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.00000 + 9.00000i −0.451697 + 0.451697i −0.895918 0.444220i \(-0.853481\pi\)
0.444220 + 0.895918i \(0.353481\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) 18.0000 18.0000i 0.896644 0.896644i
\(404\) 0 0
\(405\) 5.00000 + 10.0000i 0.248452 + 0.496904i
\(406\) 0 0
\(407\) 12.0000 12.0000i 0.594818 0.594818i
\(408\) 0 0
\(409\) 12.0000i 0.593362i −0.954977 0.296681i \(-0.904120\pi\)
0.954977 0.296681i \(-0.0958798\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 0 0
\(413\) −10.0000 10.0000i −0.492068 0.492068i
\(414\) 0 0
\(415\) −9.00000 3.00000i −0.441793 0.147264i
\(416\) 0 0
\(417\) −6.00000 6.00000i −0.293821 0.293821i
\(418\) 0 0
\(419\) 10.0000i 0.488532i 0.969708 + 0.244266i \(0.0785470\pi\)
−0.969708 + 0.244266i \(0.921453\pi\)
\(420\) 0 0
\(421\) 12.0000i 0.584844i 0.956289 + 0.292422i \(0.0944612\pi\)
−0.956289 + 0.292422i \(0.905539\pi\)
\(422\) 0 0
\(423\) −9.00000 9.00000i −0.437595 0.437595i
\(424\) 0 0
\(425\) 21.0000 3.00000i 1.01865 0.145521i
\(426\) 0 0
\(427\) 12.0000 + 12.0000i 0.580721 + 0.580721i
\(428\) 0 0
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) 30.0000i 1.44505i −0.691345 0.722525i \(-0.742982\pi\)
0.691345 0.722525i \(-0.257018\pi\)
\(432\) 0 0
\(433\) −7.00000 + 7.00000i −0.336399 + 0.336399i −0.855010 0.518611i \(-0.826449\pi\)
0.518611 + 0.855010i \(0.326449\pi\)
\(434\) 0 0
\(435\) −6.00000 2.00000i −0.287678 0.0958927i
\(436\) 0 0
\(437\) −18.0000 + 18.0000i −0.861057 + 0.861057i
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) −5.00000 −0.238095
\(442\) 0 0
\(443\) 25.0000 25.0000i 1.18779 1.18779i 0.210108 0.977678i \(-0.432619\pi\)
0.977678 0.210108i \(-0.0673814\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.00000 2.00000i 0.0945968 0.0945968i
\(448\) 0 0
\(449\) 12.0000i 0.566315i 0.959073 + 0.283158i \(0.0913819\pi\)
−0.959073 + 0.283158i \(0.908618\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) 0 0
\(453\) 10.0000 + 10.0000i 0.469841 + 0.469841i
\(454\) 0 0
\(455\) −6.00000 12.0000i −0.281284 0.562569i
\(456\) 0 0
\(457\) 17.0000 + 17.0000i 0.795226 + 0.795226i 0.982339 0.187112i \(-0.0599128\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 0 0
\(459\) 24.0000i 1.12022i
\(460\) 0 0
\(461\) 40.0000i 1.86299i 0.363760 + 0.931493i \(0.381493\pi\)
−0.363760 + 0.931493i \(0.618507\pi\)
\(462\) 0 0
\(463\) 1.00000 + 1.00000i 0.0464739 + 0.0464739i 0.729962 0.683488i \(-0.239538\pi\)
−0.683488 + 0.729962i \(0.739538\pi\)
\(464\) 0 0
\(465\) 6.00000 18.0000i 0.278243 0.834730i
\(466\) 0 0
\(467\) −21.0000 21.0000i −0.971764 0.971764i 0.0278481 0.999612i \(-0.491135\pi\)
−0.999612 + 0.0278481i \(0.991135\pi\)
\(468\) 0 0
\(469\) 18.0000 0.831163
\(470\) 0 0
\(471\) 6.00000i 0.276465i
\(472\) 0 0
\(473\) −12.0000 + 12.0000i −0.551761 + 0.551761i
\(474\) 0 0
\(475\) 24.0000 + 18.0000i 1.10120 + 0.825897i
\(476\) 0 0
\(477\) 5.00000 5.00000i 0.228934 0.228934i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) 6.00000 6.00000i 0.273009 0.273009i
\(484\) 0 0
\(485\) 7.00000 21.0000i 0.317854 0.953561i
\(486\) 0 0
\(487\) −1.00000 + 1.00000i −0.0453143 + 0.0453143i −0.729401 0.684087i \(-0.760201\pi\)
0.684087 + 0.729401i \(0.260201\pi\)
\(488\) 0 0
\(489\) 18.0000i 0.813988i
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) 6.00000 + 6.00000i 0.270226 + 0.270226i
\(494\) 0 0
\(495\) −8.00000 + 4.00000i −0.359573 + 0.179787i
\(496\) 0 0
\(497\) 6.00000 + 6.00000i 0.269137 + 0.269137i
\(498\) 0 0
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) 0 0
\(501\) 6.00000i 0.268060i
\(502\) 0 0
\(503\) 21.0000 + 21.0000i 0.936344 + 0.936344i 0.998092 0.0617480i \(-0.0196675\pi\)
−0.0617480 + 0.998092i \(0.519668\pi\)
\(504\) 0 0
\(505\) −16.0000 + 8.00000i −0.711991 + 0.355995i
\(506\) 0 0
\(507\) 5.00000 + 5.00000i 0.222058 + 0.222058i
\(508\) 0 0
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 0 0
\(511\) 10.0000i 0.442374i
\(512\) 0 0
\(513\) 24.0000 24.0000i 1.05963 1.05963i
\(514\) 0 0
\(515\) 11.0000 33.0000i 0.484718 1.45415i
\(516\) 0 0
\(517\) −36.0000 + 36.0000i −1.58328 + 1.58328i
\(518\) 0 0
\(519\) 30.0000 1.31685
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −15.0000 + 15.0000i −0.655904 + 0.655904i −0.954408 0.298504i \(-0.903512\pi\)
0.298504 + 0.954408i \(0.403512\pi\)
\(524\) 0 0
\(525\) −8.00000 6.00000i −0.349149 0.261861i
\(526\) 0 0
\(527\) −18.0000 + 18.0000i −0.784092 + 0.784092i
\(528\) 0 0
\(529\) 5.00000i 0.217391i
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 18.0000 + 18.0000i 0.779667 + 0.779667i
\(534\) 0 0
\(535\) −3.00000 + 9.00000i −0.129701 + 0.389104i
\(536\) 0 0
\(537\) 2.00000 + 2.00000i 0.0863064 + 0.0863064i
\(538\) 0 0
\(539\) 20.0000i 0.861461i
\(540\) 0 0
\(541\) 24.0000i 1.03184i 0.856637 + 0.515920i \(0.172550\pi\)
−0.856637 + 0.515920i \(0.827450\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.0000 + 36.0000i 0.771035 + 1.54207i
\(546\) 0 0
\(547\) 3.00000 + 3.00000i 0.128271 + 0.128271i 0.768328 0.640057i \(-0.221089\pi\)
−0.640057 + 0.768328i \(0.721089\pi\)
\(548\) 0 0
\(549\) 12.0000 0.512148
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 12.0000 6.00000i 0.509372 0.254686i
\(556\) 0 0
\(557\) 31.0000 31.0000i 1.31351 1.31351i 0.394704 0.918808i \(-0.370847\pi\)
0.918808 0.394704i \(-0.129153\pi\)
\(558\) 0 0
\(559\) −18.0000 −0.761319
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) 1.00000 1.00000i 0.0421450 0.0421450i −0.685720 0.727865i \(-0.740513\pi\)
0.727865 + 0.685720i \(0.240513\pi\)
\(564\) 0 0
\(565\) −9.00000 3.00000i −0.378633 0.126211i
\(566\) 0 0
\(567\) −5.00000 + 5.00000i −0.209980 + 0.209980i
\(568\) 0 0
\(569\) 12.0000i 0.503066i 0.967849 + 0.251533i \(0.0809347\pi\)
−0.967849 + 0.251533i \(0.919065\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) −6.00000 6.00000i −0.250654 0.250654i
\(574\) 0 0
\(575\) 21.0000 3.00000i 0.875761 0.125109i
\(576\) 0 0
\(577\) −19.0000 19.0000i −0.790980 0.790980i 0.190673 0.981654i \(-0.438933\pi\)
−0.981654 + 0.190673i \(0.938933\pi\)
\(578\) 0 0
\(579\) 10.0000i 0.415586i
\(580\) 0 0
\(581\) 6.00000i 0.248922i
\(582\) 0 0
\(583\) −20.0000 20.0000i −0.828315 0.828315i
\(584\) 0 0
\(585\) −9.00000 3.00000i −0.372104 0.124035i
\(586\) 0 0
\(587\) 15.0000 + 15.0000i 0.619116 + 0.619116i 0.945305 0.326188i \(-0.105764\pi\)
−0.326188 + 0.945305i \(0.605764\pi\)
\(588\) 0 0
\(589\) −36.0000 −1.48335
\(590\) 0 0
\(591\) 10.0000i 0.411345i
\(592\) 0 0
\(593\) −15.0000 + 15.0000i −0.615976 + 0.615976i −0.944497 0.328521i \(-0.893450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) 0 0
\(595\) 6.00000 + 12.0000i 0.245976 + 0.491952i
\(596\) 0 0
\(597\) 16.0000 16.0000i 0.654836 0.654836i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 9.00000 9.00000i 0.366508 0.366508i
\(604\) 0 0
\(605\) 5.00000 + 10.0000i 0.203279 + 0.406558i
\(606\) 0 0
\(607\) 7.00000 7.00000i 0.284121 0.284121i −0.550629 0.834750i \(-0.685612\pi\)
0.834750 + 0.550629i \(0.185612\pi\)
\(608\) 0 0
\(609\) 4.00000i 0.162088i
\(610\) 0 0
\(611\) −54.0000 −2.18461
\(612\) 0 0
\(613\) −9.00000 9.00000i −0.363507 0.363507i 0.501596 0.865102i \(-0.332747\pi\)
−0.865102 + 0.501596i \(0.832747\pi\)
\(614\) 0 0
\(615\) 18.0000 + 6.00000i 0.725830 + 0.241943i
\(616\) 0 0
\(617\) −15.0000 15.0000i −0.603877 0.603877i 0.337462 0.941339i \(-0.390432\pi\)
−0.941339 + 0.337462i \(0.890432\pi\)
\(618\) 0 0
\(619\) 42.0000i 1.68812i 0.536247 + 0.844061i \(0.319842\pi\)
−0.536247 + 0.844061i \(0.680158\pi\)
\(620\) 0 0
\(621\) 24.0000i 0.963087i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) −24.0000 24.0000i −0.958468 0.958468i
\(628\) 0 0
\(629\) −18.0000 −0.717707
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 0 0
\(633\) 12.0000 12.0000i 0.476957 0.476957i
\(634\) 0 0
\(635\) −15.0000 5.00000i −0.595257 0.198419i
\(636\) 0 0
\(637\) −15.0000 + 15.0000i −0.594322 + 0.594322i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −3.00000 + 3.00000i −0.118308 + 0.118308i −0.763782 0.645474i \(-0.776660\pi\)
0.645474 + 0.763782i \(0.276660\pi\)
\(644\) 0 0
\(645\) −12.0000 + 6.00000i −0.472500 + 0.236250i
\(646\) 0 0
\(647\) −9.00000 + 9.00000i −0.353827 + 0.353827i −0.861531 0.507705i \(-0.830494\pi\)
0.507705 + 0.861531i \(0.330494\pi\)
\(648\) 0 0
\(649\) 40.0000i 1.57014i
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 0 0
\(653\) −33.0000 33.0000i −1.29139 1.29139i −0.933928 0.357462i \(-0.883642\pi\)
−0.357462 0.933928i \(-0.616358\pi\)
\(654\) 0 0
\(655\) 4.00000 + 8.00000i 0.156293 + 0.312586i
\(656\) 0 0
\(657\) 5.00000 + 5.00000i 0.195069 + 0.195069i
\(658\) 0 0
\(659\) 22.0000i 0.856998i −0.903542 0.428499i \(-0.859042\pi\)
0.903542 0.428499i \(-0.140958\pi\)
\(660\) 0 0
\(661\) 12.0000i 0.466746i −0.972387 0.233373i \(-0.925024\pi\)
0.972387 0.233373i \(-0.0749763\pi\)
\(662\) 0 0
\(663\) −18.0000 18.0000i −0.699062 0.699062i
\(664\) 0 0
\(665\) −6.00000 + 18.0000i −0.232670 + 0.698010i
\(666\) 0 0
\(667\) 6.00000 + 6.00000i 0.232321 + 0.232321i
\(668\) 0 0
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) 48.0000i 1.85302i
\(672\) 0 0
\(673\) 25.0000 25.0000i 0.963679 0.963679i −0.0356839 0.999363i \(-0.511361\pi\)
0.999363 + 0.0356839i \(0.0113610\pi\)
\(674\) 0 0
\(675\) −28.0000 + 4.00000i −1.07772 + 0.153960i
\(676\) 0 0
\(677\) 27.0000 27.0000i 1.03769 1.03769i 0.0384331 0.999261i \(-0.487763\pi\)
0.999261 0.0384331i \(-0.0122367\pi\)
\(678\) 0 0
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) 22.0000 0.843042
\(682\) 0 0
\(683\) −27.0000 + 27.0000i −1.03313 + 1.03313i −0.0336941 + 0.999432i \(0.510727\pi\)
−0.999432 + 0.0336941i \(0.989273\pi\)
\(684\) 0 0
\(685\) 3.00000 9.00000i 0.114624 0.343872i
\(686\) 0 0
\(687\) 6.00000 6.00000i 0.228914 0.228914i
\(688\) 0 0
\(689\) 30.0000i 1.14291i
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 0 0
\(693\) −4.00000 4.00000i −0.151947 0.151947i
\(694\) 0 0
\(695\) 12.0000 6.00000i 0.455186 0.227593i
\(696\) 0 0
\(697\) −18.0000 18.0000i −0.681799 0.681799i
\(698\) 0 0
\(699\) 30.0000i 1.13470i
\(700\) 0 0
\(701\) 20.0000i 0.755390i −0.925930 0.377695i \(-0.876717\pi\)
0.925930 0.377695i \(-0.123283\pi\)
\(702\) 0 0
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) 0 0
\(705\) −36.0000 + 18.0000i −1.35584 + 0.677919i
\(706\) 0 0
\(707\) −8.00000 8.00000i −0.300871 0.300871i
\(708\) 0 0
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −18.0000 + 18.0000i −0.674105 + 0.674105i
\(714\) 0 0
\(715\) −12.0000 + 36.0000i −0.448775 + 1.34632i
\(716\) 0 0
\(717\) −24.0000 + 24.0000i −0.896296 + 0.896296i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 22.0000 0.819323
\(722\) 0 0
\(723\) −18.0000 + 18.0000i −0.669427 + 0.669427i
\(724\) 0 0
\(725\) 6.00000 8.00000i 0.222834 0.297113i
\(726\) 0 0
\(727\) −25.0000 + 25.0000i −0.927199 + 0.927199i −0.997524 0.0703254i \(-0.977596\pi\)
0.0703254 + 0.997524i \(0.477596\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 18.0000 0.665754
\(732\) 0 0
\(733\) 15.0000 + 15.0000i 0.554038 + 0.554038i 0.927604 0.373566i \(-0.121865\pi\)
−0.373566 + 0.927604i \(0.621865\pi\)
\(734\) 0 0
\(735\) −5.00000 + 15.0000i −0.184428 + 0.553283i
\(736\) 0 0
\(737\) −36.0000 36.0000i −1.32608 1.32608i
\(738\) 0 0
\(739\) 30.0000i 1.10357i −0.833987 0.551784i \(-0.813947\pi\)
0.833987 0.551784i \(-0.186053\pi\)
\(740\) 0 0
\(741\) 36.0000i 1.32249i
\(742\) 0 0
\(743\) 9.00000 + 9.00000i 0.330178 + 0.330178i 0.852654 0.522476i \(-0.174992\pi\)
−0.522476 + 0.852654i \(0.674992\pi\)
\(744\) 0 0
\(745\) 2.00000 + 4.00000i 0.0732743 + 0.146549i
\(746\) 0 0
\(747\) −3.00000 3.00000i −0.109764 0.109764i
\(748\) 0 0
\(749\) −6.00000 −0.219235
\(750\) 0 0
\(751\) 42.0000i 1.53260i 0.642482 + 0.766301i \(0.277905\pi\)
−0.642482 + 0.766301i \(0.722095\pi\)
\(752\) 0 0
\(753\) −4.00000 + 4.00000i −0.145768 + 0.145768i
\(754\) 0 0
\(755\) −20.0000 + 10.0000i −0.727875 + 0.363937i
\(756\) 0 0
\(757\) −9.00000 + 9.00000i −0.327111 + 0.327111i −0.851487 0.524376i \(-0.824299\pi\)
0.524376 + 0.851487i \(0.324299\pi\)
\(758\) 0 0
\(759\) −24.0000 −0.871145
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 0 0
\(763\) −18.0000 + 18.0000i −0.651644 + 0.651644i
\(764\) 0 0
\(765\) 9.00000 + 3.00000i 0.325396 + 0.108465i
\(766\) 0 0
\(767\) −30.0000 + 30.0000i −1.08324 + 1.08324i
\(768\) 0 0
\(769\) 40.0000i 1.44244i 0.692708 + 0.721218i \(0.256418\pi\)
−0.692708 + 0.721218i \(0.743582\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −9.00000 9.00000i −0.323708 0.323708i 0.526480 0.850188i \(-0.323511\pi\)
−0.850188 + 0.526480i \(0.823511\pi\)
\(774\) 0 0
\(775\) 24.0000 + 18.0000i 0.862105 + 0.646579i
\(776\) 0 0
\(777\) 6.00000 + 6.00000i 0.215249 + 0.215249i
\(778\) 0 0
\(779\) 36.0000i 1.28983i
\(780\) 0 0
\(781\) 24.0000i 0.858788i
\(782\) 0 0
\(783\) −8.00000 8.00000i −0.285897 0.285897i
\(784\) 0 0
\(785\) 9.00000 + 3.00000i 0.321224 + 0.107075i
\(786\) 0 0
\(787\) 15.0000 + 15.0000i 0.534692 + 0.534692i 0.921965 0.387273i \(-0.126583\pi\)
−0.387273 + 0.921965i \(0.626583\pi\)
\(788\) 0 0
\(789\) 18.0000 0.640817
\(790\) 0 0
\(791\) 6.00000i 0.213335i
\(792\) 0 0
\(793\) 36.0000 36.0000i 1.27840 1.27840i
\(794\) 0 0
\(795\) −10.0000 20.0000i −0.354663 0.709327i
\(796\) 0 0
\(797\) 3.00000 3.00000i 0.106265 0.106265i −0.651975 0.758240i \(-0.726059\pi\)